Average Error: 6.0 → 6.0
Time: 1.3s
Precision: binary64
\[\frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}\]
↓
\[\frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}\]
\frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}
↓
\frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}
double code(double w, double a, double d) {
	return ((double) (((double) (((double) (4.0 * w)) * a)) / ((double) (((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a)))))))) / 2.0))));
}
↓
double code(double w, double a, double d) {
	return ((double) (((double) (((double) (4.0 * w)) * a)) / ((double) (((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a)))))))) / 2.0))));
}

Error

Bits error versus w

Bits error versus a

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.0

    \[\frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}\]

  2. Final simplification6.0

    \[\leadsto \frac{\left(4 \cdot w\right) \cdot a}{\frac{1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}}{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (w a d)
  :name "(/ (* (* 4.0 w) a) (/ (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a)))) 2.0))"
  :precision binary64
  (/ (* (* 4.0 w) a) (/ (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a)))) 2.0)))